AfdelingToegepasteWiskunde/DivisionofAppliedMathematics ... · Fundamentalsandoverview SLIDE1/12...

Afdeling Toegepaste Wiskunde / Division of Applied Mathematics

Fundamentals and overview SLIDE 1/12

TW793: DIGITAL IMAGE PROCESSING

WHAT IS A (GRAY SCALE) DIGITAL IMAGE?

Matlab (command window) instructions:

>> A = [0 128; 192 255] ENTER

A =

0 128

192 255

>> image( A ) ENTER

>> colormap( gray ( 256 ) ) ENTER

>> axis image ENTER

0.5 1 1.5 2 2.5

0.5

1

1.5

2

2.5



A gray scale digital image is a

• matrix f (x, y), where

• f is the intensity (gray scale value) of the image f at row x and column y

• and each coordinate (x, y) is represented by a pixel, where

• the pixel is coloured black if f(x, y) = 0 and coloured white if f (x, y) = L− 1

(for the example on the previous page we have that L = 256)

Matlab instructions:

>> a = A(2,1) ENTER

a =

192

>> b = A(1,2) ENTER

b =

128



When colormap( gray ( 256 ) ) is selected and an image (matrix) is dis-played in Matlab with the image instruction, each entry (pixel) is internally“converted” to the uint8 (unsigned 8-bit integer) data type. This impliesthat each pixel (matrix entry) is represented with an 8-bit byte, which im-plies L = 28 = 256 possible intensity values (gray scales). The instructionimagesc is the same as image, except that the data is scaled to use the fullcolormap, which can come in very handy. Images read into memory from astorage device are often in uint8 format.

In order to be able to manipulate an uint8matrix (image) in double precisionarithmetic, the matrix has to be converted into the double data type withB = double( A ). The inverse operation is achieved with A = uint8( B ).

The Matlab default is double.

An image file, e.g. “lenna256.jpg” (JPEG format) can be displayed withthe following Matlab instruction (IP Toolbox)

>> imshow( ’lenna256.jpg’ ) ENTER



lenna256.jpg



To manipulate this image in Matlab, the following instructions are needed

>> X = imread( ’lenna256.jpg’ ); ENTER

>> XX = double( X ); ENTER

The variable X now represents a matrix that can be accessed/manipulated

>> mn = min( min( XX ) ) ENTER

mn =

0

>> mx = max( max( XX ) ) ENTER

mx =

239

>> sz = size( XX ) ENTER

sz =

256 256

>> entry = XX(100,150) ENTER

entry =

173



The matrix XX can again be displayed with the instructions

>> colormap( gray ( 256 ) ); ENTER

>> imagesc( XX ) ENTER

>> axis image ENTER

50 100 150 200 250

50

100

150

200

250

We can now, e.g., calculate and display the negative of the image with theinstructions

>> Y = max( max( XX ) ) - XX; ENTER

>> colormap( gray ( 256 ) ); ENTER

>> imagesc( Y ) ENTER

>> axis image ENTER



50 100 150 200 250

50

100

150

200

250

Any matrix can be saved to a disk. The following instruction saves thevariable Y in the current directory as the Matlab file “lenna256neg.mat”:>> save lenna256neg.mat Y ENTER

During subsequent Matlab sessions this file can be retrieved and automati-cally reassigned to the variable Y with the instruction>> load lenna256neg.mat ENTER

The matrix Y can also be saved in a variety of common image file formats,like JPEG, BMP, etc., with instructions like>> imwrite(Y,gray(256),’lenna256neg.bmp’,’bmp’)



The file “lenna256neg.bmp” (BMP format) can be displayed with the Mat-lab instruction (IP Toolbox): >> imshow(’lenna256neg.bmp’)

lenna256neg.bmp

In order to obtain a list of all the available Matlab functions in the ImageProcessing (IP) Toolbox, give the instruction: >> help images

E.g., the negative of an image can also be obtained with the imcomplement

function, i.e.: >> Y = imcomplement( X );

For a demonstration of the IP Toolbox, enter demo in the command windowand double-click on “Toolboxes” and then “Image Processing”...



WHAT IS DIGITAL IMAGE PROCESSING?

1 Input image −→ Processing −→ Output image

• Image enhancement and restoration

Input −→ Filter −→ Output

Input −→ Transform −→ Filter −→ Inverse transform −→ Output

Wiener filter

Input image Output image



• Image compression

Input −→ Coding −→ Code −→ Decoding −→ Output

JPEG Demo: 8 DCT coefficients retained



2 Image −→ Processing −→ Features −→ Recognition

• Object recognition

Image −→ Segmentation −→ Object

−→ Representation and description −→ Features −→ Recognition

Example: Signature verification

(a) (b)

(c) (d)

(a) (b)

(c) (d)

(the authentic signature is (a))



OVERVIEW OF COURSE

• Fourier analysis

• Image enhancement

{• Spatial domain (Ch. 3)• Fourier domain (Ch. 4)

• Image restoration (Ch. 5)• Colour IP (Ch. 6)Wavelets (Ch. 7)• Compression (Ch. 8)• Morphological IP (Ch. 9)

• Pattern Recognition

• Segmentation (Ch. 10)• Representation & description (Ch. 11)Object recognition (Ch. 12)

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